A first-principles-based effective Hamiltonian is used to investigate low-temperature properties of Ba(Zr,Ti)O3 relaxor ferroelectrics under an increasing dc electric field. This system progressively develops an electric polarization that is highly nonlinear with the dc field. This development leads to a maximum of the static dielectric response at a critical field, Eth, and involves four different field regimes. Each of these regimes is associated with its own behavior of polar nanoregions, such as shrinking, flipping, and elongation of dipoles or change in morphology. The clusters propagating inside the whole sample, with dipoles being parallel to the field direction, begin to form at precisely the Eth critical field. Such a result, and further analysis we perform, therefore, reveal that field-induced percolation of polar nanoregions is the driving mechanism for the transition from the relaxor to ferroelectric state. \textcopyright 2013 American Physical Society.